Warm Up Evaluate each expression for the given values of the variables. 1. 2x – 3y for x = 17 and y = 6 2. 5(x + 3) + 4y for x = 3 and y = 2 3. 6.9(x – 2.7) + 7.1 for x = 5.1 4. 5x – 4y for x = 0.3 and y = 0.2 16 38 23.66 0.7

Integers: the set of whole numbers and their opposites. Opposites (additive inverses): numbers that are the same distance from 0, but on opposite sides of 0 on the number line.

Example 1: Sports Application Use <, >, or = to compare the scores. A. Aaron’s score is 4, and Felicity’s score is –1. Place the scores on the number line. –5 –4 –3 –2 –1 0 1 2 3 4 5 • • –1 < 4 –1 is to the left of 4.

Additional Example 1: Sports Application Use <, >, or = to compare the scores. B. List the golf scores in order from the lowest to the highest. The scores are –4, 2, 5, and –3. Place the scores on the number line and read them from left to right. –5 –4 –3 –2 –1 0 1 2 3 4 5 • • • • In order from the lowest score to the highest score, the scores are –4, –3, 2, and 5.

Use <, >, or = to compare the scores. Check It Out: Example 1 Use <, >, or = to compare the scores. A. Fran’s score is –2, and Joaquin’s score is –3. Place the scores on the number line. • –5 –4 –3 –2 –1 0 1 2 3 4 5 • –3 < –2 –3 is to the left of –2.

Use <, >, or = to compare the scores. Check It Out: Example 1 Use <, >, or = to compare the scores. B. List the golfer’s scores in order from the lowest to the highest. The scores are –3, 1, 0, and –2. Place the scores on the number line and read them from left to right. –5 –4 –3 –2 –1 0 1 2 3 4 5 • • • • In order from the lowest score to the highest score, they are –3, –2, 0, and 1.

Example 2: Ordering Integers Write the integers 8, –5, and 4 in order from t least to greatest. Compare each pair of integers. 8 > –5, 8 > 4, and –5 < 4 –5 is less than both 4 and 8. –5, 4, and 8.

Check It Out: Example 2 Write the integers 7, –12, and 13 in order from least to greatest. Compare each pair of integers. 13 > –12, 13 > 7, and –12 < 7 –12 is less than both 7 and 13. –12, 7, and 13.

Example 3: Finding Additive Inverses Find the additive inverse of each integer. A. 6 –6 –6 is the same distance from 0 as 6 is on the number line. B. –14 14 14 is the same distance from 0 as –14 is on the number line. C. 0.5 –0.5 –0.5 is the same distance from 0 as 0.5 is on the number line.

Check It Out: Example 3 Find the additive inverse of each integer. A. 12 –12 –12 is the same distance from 0 as 12 is on the number line. B. –1.9 1.9 1.9 is the same distance from 0 as –1.9 is on the number line. C. 1 –1 –1 is the same distance from 0 as 1 is on the number line.

absolute value: the distance from 0 on a number line. always positive or 0 “The absolute value of –4” is written as |–4| Additive inverses have the same absolute value. 4 units 4 units –5 –4 –3 –2 –1 0 1 2 3 4 5 –4 = 4 = 4. Both 4 and –4 are 4 units from 0.

Example 4: Simplifying Absolute-Value Expressions Simplify each expression. A. –8 + –5 –8 = 8 –8 is 8 units from 0. –5 = 5 –5 is 5 units from 0. 8 + 5 = 13 B. 5 – 6 –1 = 1 –1 is 1 units from 0.

Check It Out: Example 4 Simplify each expression. A. –2 + –9 –2 = 2 –2 is 2 units from 0. –9 = 9 –9 is 9 units from 0. 2 + 9 = 11 B. 1 – 1 0 = 0 0 is 0 units from 0.

Lesson Quiz Write the integers in order from least to greatest. 1. –17, –26, 23 2. 0, 5, –4 Simplify each expression. 3. The sum of 3 and the additive inverse of –8 4. |–4| + |–2| 5. At the end of the course, your golf score was –2. Your friend’s score was 7. Use <, >, or = to compare the scores. –26, –17, 23 –4, 0, 5 11 6 –2 < 7